Question 352231
Let the shortest leg be {{{x}}}.
{{{x^2+(x+7)^2=(x+14)^2}}}
{{{x^2+x^2+14x+49=x^2+28x+196}}}
{{{2x^2+14x+49=x^2+28x+196}}}
{{{x^2-14x-147=0}}}
Factor
{{{(x-21)(x+7)=0}}}
Only the positive solution makes sense in this problem.
{{{x-21=0}}}
{{{x=21}}}inches
.
.
.
{{{A=(1/2)x(x+7)}}}
{{{A=(1/2)(21)(28)}}}
{{{highlight(A=294)}}}sq.in.